Find the exact value without using the calculator To receive

Find the exact value, without using the calculator. To receive full credit, you must use a sketch, locating the angle in the appropriate quadrant State your answer in radian measure. If the solution does not exist, you must explain why. sin^-1 (-2) cos^-1(- 1/2) sin^-1 (cos (5 pi/4)) Evaluate: CSC (arcos x/5)

Solution

a) y = sin^-1(-2)

siny = -2

Range : -1<=siny<=1.

So no solution exist

b) y = cos^-1(-1/2)

cosy = -1/2

y = pi -pi/3 ( As Range of cos^-1x lies in [ 0, pi] )

So, y = 2pi/3

Angle lies in IInd quadrant

c) y = sin^-1(cos(5pi/4)

siny = cos5pi/4

siny = -1/sqrt2

Range of sin^-1x : [-pi/2 , pi/2]

y = sin^-1(-1/sqrt2)

= - pi/4

y = -pi/4 lies in IVrt quadrant